Finally, we discuss some mechanisms not included in the above calculation. The back reaction of the condensate to the metric is negligible in Ref. [1]}, due to the small energy density of the scalar field. The self-interaction of the scalars changes the shape of the wavefunctions, even causing bosenova before a mode reaches its maximum mass. Numerical simulation shows that the bosenova collapse happens when the scalar cloud to BH mass ratio \(M_s/M\)  is approximately \(0.16\)  [2]}. From the calculations above, this ratio is always less than \(0.0668\)  without accretion but could reach as much as \(0.34\)  if accretion is present. The study of the BH-condensate evolution with bosenova is beyond the scope of this work.
